M. Droste and P. Gastin, On recognizable and rational formal power series in partially commuting variables. Automata, languages and programming (Bologna, 1997. Home/Search Document Not in Database Summary Related Articles Check |
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Commutation Problems on Sets of Words and Formal Power Series - Petre (2002) (Correct)
....tzenberger proved in [72] that the rational power series coincide with the recognizable power series in noncommuting variables. It turned out however, that in general, the recognizable and rational series do not coincide, see, e.g. 55] and [71] In particular, Droste and Gastin considered in [19] the recognizable series over trace monoids, i.e. series in partially commuting variables. They characterized in the same paper the recognizable series as being the m c rational series, when the semiring of coefficients is commutarive, thus extending to series Ochmafiski s result on recognizable ....
....as being the m c rational series, when the semiring of coefficients is commutarive, thus extending to series Ochmafiski s result on recognizable languages over trace monoids, see [55] A free commutative monoid is obviously a trace monoid. In this case, the recognizable series are included, by [19], in those rational series for which the star operation is restricted to series having the support included in a , for some a . This proves that the recognizable series are strictly included in the rational series; e.g. ab) is an N rational series which is not recognizable by the above ....
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M. Droste and P. Gastin, On recognizable and rational formal power series in partially commuting variables. Automata, languages and programming (Bologna, 1997.
Annual progress report ALAPEDES - Contract Erb--Fmrx--Ct (Correct)
....to use automaton theory to study problems related to the control of discrete event systems. In LIAFA, some work has been done on the theoretical problems underlying T 4. Droste and Gastin have been working on formal power series in partially commuting variables. Droste and Gastin chracterize in ([29]) the recognizable formal power series over arbitrary semi rings and in partially commuting variables, i.e. over trace monoids. This provides a joint generalization of two very classical results: Schutzenberger s and Ochm anski s theorems. The relevance of this work to T 4 is due to the central ....
M. Droste and P. Gastin. On recognizable and rational formal power series in partially commuting variables. In LNCS, editor, Proceedings of the 24th International Colloquium on Automata, Languages and Programming (ICALP'97). Springer-Verlag, 1997. To appear. Submitted to IEEE-TAC.
Modeling and Analysis of Timed Petri Nets Using Heaps of Pieces - Gaubert, Mairesse (1999) (2 citations) (Correct)
....0 ) M(a) rs M 0 (a) mm 0 : 18) Due to the commutations in (4) and (17) M 00 (a)M 00 (b) M 00 (b)M 00 (a) for all (a; b) 2 I. This implies that y G , seen as a function from the trace monoid T = Rmax , is recognizable. Such functions are well studied objects, see [19] and the chapter of Duchamp and Krob in [18] Remark VI.4: As it was discussed above, the dimension of H is the number of places (normal representation) or approximately the number of tokens (reduced realization) of the Petri net G. On the other hand, the dimension of B can be extremely large, ....
M. Droste and P. Gastin. On recognizable and rational formal power series in partially commuting variables. Proceedings of ICALP'97, number 1256 in LNCS, p. 682-692, 1997.
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